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    Continued fractions and the Thomson problem by Pablo Moscato, Mohammad Nazmul Haque, Anna Moscato

    Published 2023-05-01
    “…Using 453 putative optimal configurations, we searched for approximations of the form $$E(n) = (n^2/2) \, e^{g(n)}$$ E ( n ) = ( n 2 / 2 ) e g ( n ) where g(n) was obtained via a memetic algorithm that searched for truncated analytic continued fractions finally obtaining one with Mean Squared Error equal to $${5.5549 \times 10^{-8}}$$ 5.5549 × 10 - 8 for the model of the normalized energy ( $$E_n(n) \equiv e^{g(n)} \equiv 2E(n)/n^2$$ E n ( n ) ≡ e g ( n ) ≡ 2 E ( n ) / n 2 ). …”
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